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- a In the Td point group, an S41 improper rotation is equivalent to what other improper rotation? b In the D6h point group, the symmetry operation labeled C21 is equivalent to what other symmetry operation?Determine which single symmetry operation of the following point groups is equivalent to the given combination of multiple symmetry operations. a In C2v, C2v=? b In C2h, iC2=? c In D6h, C6h=? d In D2d, C2C2=? e In Oh, iS4=?Assume that x- polarized light can be assigned an E symmetry species in a system that has C4v symmetry. Can a transition from E state to a B2 state occur? Why or why not?
- Construct the symmetry-adapted linear combination molecular orbitals for hydrogen sulfide, H2S.Determine if the following integrals can be nonzero if the molecular or atomic system has the given local symmetry. Use the great orthogonality theorem if necessary. a AuOB2uAud in D2h symmetry b A1OA1A2d in C3v symmetry c g+Oggd in Dh symmetry d EOA2T1d in Td symmetryPoint groups are called such because all of the symmetry elements in the group intersect at one point in space. For point groups that have i as a symmetry operation, why must i be at that point?
- Identify the symmetry elements present in the following objects. a The Eiffel Tower. You may have to look up a picture of it if you dont remember its shape b Any book ignore the printing. c An octagonal wood block. d A jack from the set of jacks pictured here: Note that some of the points end differently.Determine the symmetry species of the D3h point group for the sp2 hybrid orbitals, assuming that the C3 axis is coincident with the z-axis and that one of the orbitals lies along the positive x-axis. See Example 13.16.Identify the symmetry elements present in the following objects. a A ream of blank paper, no holes. b A ream of blank three-holed paper. c A round pencil, unsharpened, with cylindrical eraser. d A round pencil, sharpened, with cylindrical eraser.
- In your own words, explain why an object that has more symmetry elements is said to have higher symmetry than an object with fewer symmetry elements.Without using the great orthogonality theorem, reduce the given irreducible representation in C2v symmetry. Does your answer make sense? EC25555Determine the D3h symmetry species of the sp3d hybrid orbitals, assuming that the C3 axis is coincident with the z-axis and that one of the orbitals lies along the positive x-axis. See Example 13.16.